Conductor in a Uniform Field Question

I have a question related to the attached picture. A length of wire with a current I_wire flowing through producing a surrounding B field density (B2) is placed in a uniform magnetic field with a direction as shown and a density of B1. The resultant force developed on the bar produces a linear or rotational motion of the wire. My question is if B2 is equal to or greater than the uniform field B1 will a Voltage potential still be developed along the wire? Does this change if the wire moves linearly in the direction of the applied force or rotates about a central axis?

EMF is always induced across a conductor if it moves in a magnetic field and 'cuts' the magnetic lines.

Assuming the ends of the conductor move at the same speed in both the linear and rotational motion, the voltage induced by the linear motion will differ by the rotational motion. This is because in the linear motion all the points along the conductor move at the same speed, whereas, in the rotational motion the points along the conductor move at different speeds.

v=ω*r

To find the induced EMF for the rotating conductor you need to integrate EMF=Bul from 0 to l.

I would be very careful with this one, especially as it it not a complete circuit. Will a voltage be produced along the wire? Several things can produce this: the B field and motion, charge seperation, and however the constant current is produced. The voltage produced is the sum of them all? Oh and are we in steady state? Lets assume so. What is the resistance of the wire. Lets take it as 0. Then there is no E field in the wire and no potential difference across its ends no matter what. Other assumptions will give different answers.